# Tagged Questions

For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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### Find the Langitude and Longitude of the centre point of a circle given a point on the circumference.

I couldn't find a similar question! Given I have the latitude and longitude (x,y) of a point on the circumference of a circle, and I want the circumference to be 1000m. An example of a lat lang I ...
1answer
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### Angle between a line and a circle that it goes though

I just solved a task regarding the angle under which a certain line goes through a circle. The line naturally has two common points with the circle. It seems that the angle between them is the same in ...
1answer
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### Perspective projection of a circle: what is the size of the semi-major axis?

It can be proven that the perspective projection (or camera projection) of a circle is an ellipse. But I also need to prove that the semi-major axis has the same size as the radius of the original ...
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### Geometry: Circle inscribed in square

A circle is inscribed in a square $ABCD$ of side length $2$. There is a point $P$ on the circle such that $PA=a$. Is it possible to find $PB,PC,PD$ in terms of $a$? I haven't solved a problem like ...
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### find the minimum distance between a point and border of a circle

I have a circle with radius $R$ and center $(x,y)$ and I have the coordinate of a point; I want to find the minimum path between this point and the border of circle. Here is a picture of what I said: ...
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### Translate a point on a circumference

If I have a point $A$ on the circumference of a circle with origin $O$ and radius $r$, how would I find the coordinates of point $B$, which is also on that circumference, but is $d$ units away from ...
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### Circle equation

Definition of problem: Write the circle equation which touches the coordinate axis and cross the point $M(2,1).$ I'm confused because I'm used to solve problems with given center but in this ...
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### How to find center of a circle from only an arbitary arc of that circle

How to find the center of a circle with given an arbitrary arc. we only have the arc nothing else. Is there any known equation or way to complete the circle.
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### Rewrite a circle's equation to easily see centre and radius

$$x^{2}+y^{2}-5x-15y+30=0$$ I'm supposed to rewrite this equation so that you can easily see the centre and radius of the circle. I don't even know where to start. According to Mathematica the centre ...
1answer
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### Prove that the intersection of $BM$ and $CN$ is on the circumcircle of triangle $ABC.$

Let $P$ and $Q$ be on segment $BC$ of an acute triangle $ABC$ such that $\angle PAB$ = $\angle BCA$ and $\angle CAQ = \angle ABC$.Let $M$ and $N$ be the points on $AP$ and $AQ$, respectively, such ...
2answers
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### What is the equation for this wave?

So it would be hard to describe it, it's better to see it yourself: http://physics.info/waves/surface-wave.html (Angular velocity of rotating points is constant I presume) What is it called? What ...
2answers
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### Equation of circle orthogonal with $2$ given circles

Find the minimum radius of a circle which is orthogonal with both the circles: $C_1: x²+y²-12x+35=0$ and $C_2: x²+y²+4x+3=0$. I know about the condition for a circle to be orthogonal to a given ...
2answers
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### Circles- finding radii of smallest and largest circle

If $r_1$ and $r_2$ are the radii of smallest and largest circle which passes through $(5,6)$ and touches the circle $(x-2)^2+y^2=4$. Then $r_1r_2$ = ??
1answer
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### Question regarding characters and point open topology

I was wondering why the following claim is correct: Let G* be the group of all continuous homomorphisms from the topological group G and the unit circle (call it T). Then G* is an intersection of a ...
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### Minimal circle containing set of points

Suppose that there are $n$ points in the plane $x_1, x_2, \dots x_n$, and $C$ is the minimal circle (the circle with the minimal radius) that contains all of them. If there is another point $p$ ...
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### Complex number - locus of a point

Question: If argument of $\frac{z - z_1}{z-z_2}$ is $\pi\over4$, find the locus of $z$. $$z_1 = 2 + 3i$$$$z_2 = 6 + 9i$$ Approach: I tried to solve the equation using diagram, basically ...
1answer
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### Nine-point circle equivalent for tetrahedrons?

Nine-point circle for a triangle is defined as the circle that passes through: the midpoint of each side the foot of each altitude the midpoint of the line segment from each vertex to the ...
1answer
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### complex coordinates of perpendicular chords on unit circle

I am faced with the following problem.. Consider three points $A (a), B (b), C(c)$ on the unit circle $|a|= |b|= |c|=1$. Find the complex coordinates of the point $D (d)$, where $D$ also lies on the ...
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### Equation of a circle using rational fractions

Why does the following equation draw a circle ? $$\left(\frac{t^4-6t^2+1}{t^4+2t^2+1},\frac{4t-4t^3}{t^4+2t^2+1}\right),|t|\le1$$ Does it draw a perfect circle, or an approximation ? On Desmos, it ...
2answers
178 views

### Circle tangent to two other circles

How can i find a circle that is tangent to two circles which have the same center? Specifically i'm looking for a circle that will contain the smaller circle. I know how to find the circle whose ...
1answer
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### How to find out circumference of circle with given centres and radius is completely covered by other intersecting circles with same radius

I want to find whether the circumference of a circle with given centre and radius is completed covered by two or more circles with given centre and same radius in matlab
1answer
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### Rotation of a circle over another circle

Let the circle $d$ rotates over the circle $c$. If the angle rotation to be of 0 to 360, then how many times does the circle $d$ rotate during that process? Since the total external angle is 360, I ...
1answer
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### Subtracting equations of two circles which don't intersect

Suppose you subtract the equations of two circles that do not intersect. In doing so, you will obtain a line which is an "extraneous solution set". Is there any geometric significance to this line?
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### How can I find the centre of a circle given a segment with compass and straight edge only

I need to find the centre of a circle for which I have a segment with the bisection of the chord. I know the centre must lie on the perpendicular bisector, but I need to know how far down. I need to ...
2answers
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### working backwards from $\pi r^2$

I have been dipping my toes into a bit of calculus (through the better explained website), however I have become stuck on my understanding of the area of a circle. I understand that the formula for ...
1answer
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### How do I find the coordinates of 10 points spaced equally on a circle?

I am not extremely good at math but I am working with computer graphics and I need to find a way to cut a circle equally in to 10 sections. To do this I need to define 10 points on the circle and my ...
3answers
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### Coordinate of the excentre of a triangle

I am just wondering that how the coordinate of the excentre comes out if we know the coordinates of vertices of the triangle.
1answer
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### Optimisation problem - circle and square

A piece of wire of length $20$cm is cut into $2$ parts. the first part is bent into a circle of radius $r$ in cm, the second into a square of side length $s$ in cm. a) write down an expression for ...
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### How to bound the great-circle distance of two points on a sphere, only given their euclidean distance?

Suppose I have a great-circle of a sphere in $\mathbb{R}^n$, the chord length (the euclidean distance of any two points) is $L$, how can we upper bound the arc length $C$ (for any radius)? I read ...
2answers
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### How does the circumference of the top + bottom sides of a cylinder effect our calculations when working out the surface area?

I was watching a video tutorial on khan academy, (I've included the link at the bottom), and the question states that there is a 8cm cylinder, with a radius of 4. Part of the video shows a worked ...
1answer
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### formula to calculate number of arch with certain angel could be fixed in a circle

I'm looking looking for a formula to calculate how many arches with certain angle could be fixed around a circle or in circular formation. I want to use that formula to write a procedure for MSWlogo ...
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### Coloring a circle

A circular spintop is colored in blue, red and green. Whenever the spintop is rotated 120 degrees, the pattern of colors looks exactly the same, only that blue becomes red, red becomes green and green ...
1answer
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